The present invention relates to a multilevel diffractive optical element (DOE), in particular to a computer generated phase DOE, comprising a substrate with a substantially periodic transmissive or reflective relief pattern of phase retardation zones.
Computer generated DOEs of the above kind are capable of performing complicated phase transformations of a radiation wave incident thereon such as a conversion of incident radiation wavefront having one shape into a wavefront of any other shape. DOEs of the specified kind are-usually designed to have a high diffraction efficiency at a predetermined, most often, first diffraction order.
In order to obtain 100% diffraction efficiencies, DOEs suggested by Jordan et al and known as kinoforms have a periodic blazed surface relief with phase zones having a continuous profile (xe2x80x9cKinoform lensesxe2x80x9d, Appl. Opt., 9/8, August 1970, pp. 1883-1887). The depth of the phase zones in kinoforms is generally proportional to phase residues after modulo 2xcfx80 so that, in each phase zone, phase variations range is from 0 to 2xcfx80. However, it is practically very difficult to produce high quality kinoforms with properly shaped continuous blazed profile.
It has, therefore, been suggested to quantize the ideal continuous phase profile of the DOEs into discrete phase levels as an approximation to the continuous profile. Manufacturing of such a multilevel DOE is based on a generation of a plurality of binary amplitude masks and their serial use for serial etching of a plurality of levels over the entire optical element. Thus, for example, a multilevel DOE disclosed in U.S. Pat. No. 4,895,790, is produced by means of M masks in M serial manufacturing cycles so that, at each manufacturing cycle, each previously produced level is divided into two levels with a smaller distance therebetween. Thereby, in each phase zone of the DOE, there are produced N=2M levels spaced by identical distances having boundaries defining equiphase areas of the DOE. However, due to the fact that in such a multilevel DOE, all the phase zones have identical depth and number of phase levels, an amplitude of the diffracted wavefront cannot be changed independently of its phase and therefore, a desired distribution of overall diffraction efficiency of such a DOE cannot be achieved. Furthermore, when a multilevel DOE of the above kind has a varying grating period, such as for example in case of high numerical aperture diffractive lenses, maximal local diffraction efficiencies cannot be simultaneously obtained from all the phase zone, whereby overall diffraction efficiency of the DOE is reduced.
To provide for an independent control of an amplitude of diffracted wavefront, in a binary DOE, Brown, B. R. and Lohmann, A. W. have suggested a DOE in which the amplitude of the diffracted wavefront is controlled by an appropriate choice of the ratio between the widths of the levels (Brown, B. R. and Lohmann, A. W., xe2x80x9cComplex spatial filtering of binary masksxe2x80x9d, Applied Optics, 5, 6/1996, p.967). However, with the number of phase levels being limited to two, the diffraction efficiency of the DOE cannot exceed 40.5%.
It is the object of the present invention to provide a new computer generated multilevel phase diffractive optical element, in which local diffraction efficiencies and consequently an overall diffraction efficiency can be arbitrarily controlled in the range from 0 to nearly 100% over the entire element.
In the following description and claims the term xe2x80x9cprofilexe2x80x9d used with respect to a multilevel phase zone of a diffractive optical element means a line passing through extremities of phase levels of the phase zone. The term xe2x80x9cmodulation depthxe2x80x9d of a multilevel phase zone means a distance from the uppermost level of the phase zone to a base of the diffractive optical element. The term xe2x80x9coptimal modulation depthxe2x80x9d with respect to a multilevel phase zone means a modulation depth proportional to phase residues after modulo 2xcfx80, which the phase zone would have in order to ensure 100% diffraction efficiency in an m-th diffraction order, if the phase zone were continuous rather than multilevel. When a multilevel phase zone has such an optimal modulation depth, an angle of inclination of its profile with respect to the base of the diffractive optical element is optimal and a diffraction efficiency provided thereby is nearly 100% The term xe2x80x9clocalxe2x80x9d with respect to any feature of a diffractive optical element is used to designate a magnitude or value which this feature has at one specific location of the diffractive element. Thus, for example, a local modulation depth of a phase zone is a modulation depth seen in a cross-sectional view of the phase zone taken at one location along the extension thereof.
In accordance with the present invention there is provided a multilevel diffractive optical element comprising a base and a plurality of phase zones defined by a modulation depth and a number of phase levels, the number of the phase levels per phase zone varying at different locations of the element, characterised in that the variation of said number of phase levels is such that the modulation depth, at said different locations, varies in a predetermined manner of the element.
Thus, by the appropriate choice of local modulation depth, according to the present invention, it is ensured that at each location of the diffractive optical element, the phase zone profile is inclined with respect to the base of the element in such a manner that a local amplitude of the diffracted wavefront and, consequently, a local diffraction efficiency obtained from the diffractive optical element, at each said location thereof, have predetermined values.
The required orientation of the phase zone profile may be achieved by pivoting of a profile which forms with the base of the DOE an optimal in angle, around its central point or one of its edge points or any other, arbitrarily chosen point.
Thus, by virtue of variation of the modulation depth over the entire Ad element, e.g. from phase zone to phase zone and/or within one phase zone i along the direction of the extension thereof, any required distribution of diffraction efficiency of the element can be achieved. Particularly, it can be provided that, at any location of the DOE, a local diffraction efficiency in the desired order is nearly 100%. This will happen in case when, at said location of the element, the local modulation depth is of its optimal magnitude.
The local modulation depth at each location of the element is defined by the local number of phase levels at this location and by the distance therebetween. Due to the fact that, in practice, it is extremely complicated to form DOEs having variable distances between levels, in the DOE according to the present invention the distance between phase levels is preferably invariant over the entire element.
In order to determine a specific magnitude of the distance between phase levels it should be kept in mind that the smaller the distance between phase levels, the greater the number of phase levels which is required for the provision of a desired modulation depth and that, in order to render the manufacturing of the DOE less complicated and to reduce fabrication errors and scatter noise, it is clearly desirable to minimize the number of phase levels and, consequently to choose a maximal possible distance therebetween. On the other hand, to obtain required diffraction efficiencies, the number of phase levels should not be unduly minimized and therefore, the distance between levels must be sufficiently small, being however not less than that dictated by manufacturing constrains.
In view of the above, it is suggested. according to the present invention, that the distance between phase levels has an optimized magnitude determined as a distance between phase levels of a phase zone in which dopt/Nmin is of a minimal value, where dopt is a local optimal modulation depth of the phase zone and Nmin is a minimal local number of levels which this phase zone needs to have in order to achieve the predetermined local diffraction efficiency.
In a preferred embodiment of the present invention, the DOE is adapted for production via the use of M masks in M serial manufacturing cycles, a maximal number of phase levels obtained thereby being 2M.
It is the advantage of the present invention that, with the DOE being produced in the above manner, any distribution of the modulation depth and, consequently, any desired distribution of overall diffraction efficiency of the DOE can be achieved.
In accordance with the present invention, there is further provided a method for producing a multilevel diffractive optical element having a phase function xcfx86=xcfx86 (x,y) and phase zones of different local modulation depth d=d (x,y) defined by different local number of phase levels, the phase levels having substantially identical distance h therebetween, said method comprising:
generating a plurality of M binary amplitude masks including the multilevel information, the masks being configured to provide, in each phase zone, its local number of phase levels, the number of masks being defined by an integer N0 which is at least not less than a maximal number of phase zone levels per phase zone over the optical element and
utilizing the masks"" information serially for serial etching of said phase levels into said phase zones of the optical element,
a binary amplitude transmittance of the masks being defined as:       T    M    =      t    ⁢          {              sin        ⁢                  xe2x80x83                ⁢                  (                      P            ⁢                          xe2x80x83                        ⁢                          Mod              ⁡                              [                                  Φ                                      2                    ⁢                                          xe2x80x83                                        ⁢                    π                                                  ]                                      ⁢                          d                              d                0                                              )                    }      
where P is a parameter which is defined by a serial number of a mask. i.e.
P=P(M). and which determines a number of boundaries of phase levels provided in each phase zone by this mask, and d0 is a maximal achievable modulation depth:
d0=N0xc2x7h
Preferably, the etching depths for the masks are related by a fixed ratio. Thus. with the DOE being produced in a manner similar to that described in U.S. Pat. No. 4,895,790, P=2Mxe2x88x921 and the etching depth produced by a mask is twice the etching depth produced by the preceding mask. If any other method of determining the etching depths of the masks is used, the parameter P will be defined accordingly.
Preferably, the distance h between the phase levels is determined by:
calculating for each phase zone, an optimal local modulation depth, which the phase zone would have, in order to ensure 100% local diffraction efficiency in the m-th diffraction order, if the phase zone profile were continuous rather than multilevel;
assuming that all the phase zones have their optimal local modulation depths and the distance between the phase levels in the phase zones is a free parameter, calculating local minimal numbers of phase levels which are required to provide for the desired distribution of the diffraction efficiency;
calculating local distances between the phase levels as a result of a division of the optimal local modulation depth of each phase zone by the minimal local number of levels thereof, the local distance of a minimal magnitude being chosen as the optimized distance between the phase levels for the entire optical element.